TOPIC - PROBABILITY(MATHS)

                        PROBABILITY 

Probability in mathematics is a measure of the likelihood that an event will occur. It's a numerical value between 0 and 1, where 0 represents impossibility and 1 represents certainty. Probability is used to quantify uncertainty and make predictions about the likelihood of different outcomes. 

Key Concepts:

Event: A specific outcome or set of outcomes in a random experiment. 

Sample Space: The set of all possible outcomes of an experiment. 

Probability of an Event: The ratio of favorable outcomes to the total number of possible outcomes. 

Types of Probability: Classical, empirical, subjective, and axiomatic probability. 

Rules of Probability: Addition rule, multiplication rule, and complement rule. 

Formulas:

Basic Probability: P(A) = (Number of favorable outcomes for event A) / (Total number of possible outcomes) 

Addition Rule: P(A or B) = P(A) + P(B) - P(A and B) 

Complement Rule: P(not A) = 1 - P(A) 

Conditional Probability: P(B|A) = P(A and B) / P(A) 

Multiplication Rule (for independent events): P(A and B) = P(A) * P(B) 

Examples:

Coin Toss: The probability of flipping heads is 1/2, as there are two equally likely outcomes (heads or tails). 

Rolling a Die: The probability of rolling a 6 on a standard six-sided die is 1/6. 

Drawing a Card: The probability of drawing a red card from a standard deck of 52 cards is 26/52 or 1/2.